def test_hf_state_plane_wave_basis_lowest_single_determinant_state(self): grid_length = 7 dimension = 1 spinless = True n_particles = 4 length_scale = 2.0 grid = Grid(dimension, grid_length, length_scale) hamiltonian = jellium_model(grid, spinless) hamiltonian_sparse = get_sparse_operator(hamiltonian) hf_state = hartree_fock_state_jellium(grid, n_particles, spinless, plane_wave=True) HF_energy = expectation(hamiltonian_sparse, hf_state) for occupied_orbitals in permutations([1] * n_particles + [0] * (grid_length - n_particles)): state_index = numpy.sum(2**numpy.array(occupied_orbitals)) HF_competitor = numpy.zeros(2**grid_length) HF_competitor[state_index] = 1.0 self.assertLessEqual( HF_energy, expectation(hamiltonian_sparse, HF_competitor))
def test_hf_state_energy_close_to_ground_energy_at_high_density(self): grid_length = 8 dimension = 1 spinless = True n_particles = grid_length**dimension // 2 # High density -> small length_scale. length_scale = 0.25 grid = Grid(dimension, grid_length, length_scale) hamiltonian = jellium_model(grid, spinless) hamiltonian_sparse = get_sparse_operator(hamiltonian) hf_state = hartree_fock_state_jellium(grid, n_particles, spinless, plane_wave=True) restricted_hamiltonian = jw_number_restrict_operator( hamiltonian_sparse, n_particles) E_g = get_ground_state(restricted_hamiltonian)[0] E_HF_plane_wave = expectation(hamiltonian_sparse, hf_state) self.assertAlmostEqual(E_g, E_HF_plane_wave, places=5)
def test_hf_state_energy_same_in_plane_wave_and_dual_basis(self): grid_length = 4 dimension = 1 wigner_seitz_radius = 10.0 spinless = False n_orbitals = grid_length**dimension if not spinless: n_orbitals *= 2 n_particles = n_orbitals // 2 length_scale = wigner_seitz_length_scale(wigner_seitz_radius, n_particles, dimension) grid = Grid(dimension, grid_length, length_scale) hamiltonian = jellium_model(grid, spinless) hamiltonian_dual_basis = jellium_model(grid, spinless, plane_wave=False) # Get the Hamiltonians as sparse operators. hamiltonian_sparse = get_sparse_operator(hamiltonian) hamiltonian_dual_sparse = get_sparse_operator(hamiltonian_dual_basis) hf_state = hartree_fock_state_jellium(grid, n_particles, spinless, plane_wave=True) hf_state_dual = hartree_fock_state_jellium(grid, n_particles, spinless, plane_wave=False) E_HF_plane_wave = expectation(hamiltonian_sparse, hf_state) E_HF_dual = expectation(hamiltonian_dual_sparse, hf_state_dual) self.assertAlmostEqual(E_HF_dual, E_HF_plane_wave)